Spectral Functions in Holographic Renormalization Group Flows

TL;DR

This paper investigates the spectral functions in holographic RG flows, revealing continuous spectra with unique features like peaks and oscillations, and confirms their consistency with conformal dimensions in dual theories.

Contribution

It provides numerical calculations of spectral functions in specific holographic RG flows, highlighting their continuous nature and characteristic features across UV and IR fixed points.

Findings

Spectral functions are continuous in holographic RG flows.

Features include sharp peaks and oscillations in the UV.

Spectral functions match conformal dimensions in UV and IR.

Abstract

The spectrum of two-point functions in a holographic renormalization group flow from an ultraviolet (UV) to an infrared (IR) conformal fixed point is necessarily continuous. For a toy model, the spectral function does not only show the expected UV and IR behaviours, but other interesting features such as sharp peaks and oscillations in the UV. The spectral functions for the SU(3)xU(1) flow in AdS_4/CFT_3 and the SU(2)xU(1) flow in AdS_5/CFT_4 are calculated numerically. They exhibit a simple cross-over behaviour and reproduce the conformal dimensions of the dual operators in the UV and IR conformal phases.